Column n gives the trajectory of iterates of A049820, when starting from A045765(n), thus stepping through successive parent-nodes when starting from the n-th leaf in the tree generated by edge-relation A049820(child) = parent, until finally reaching the fixed point 0, which is the root of the whole tree.

A portion of the hanging tail of each column (upward from the first encountered zero) converges towards A259934, although not in monotone fashion.